The discovery of topological insulators has created a revolution in condensed matter science that has far ranging implications over coming decades. I will introduce a simplest way to understand the “periodic table” for topological phases, and apply these ideas to semimetals, insulators, and superconductors. In the superconductor case, a Majorana Kramers pair may appear on the boundary and induces unprecedented fractional Josephson effects. These effects indicate the existence of a “periodic building” for topological phases, with the aforementioned table being its ground floor. Strong connections will be made to ongoing experiments and related topics.